+
+include "logic/equality.ma".
+(* Inclusion of: GRP512-1.p *)
+(* -------------------------------------------------------------------------- *)
+(* File : GRP512-1 : TPTP v3.1.1. Bugfixed v2.7.0. *)
+(* Domain : Group Theory (Abelian) *)
+(* Problem : Axiom for Abelian group theory, in product and inverse, part 4 *)
+(* Version : [McC93] (equality) axioms. *)
+(* English : *)
+(* Refs : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit *)
+(* : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(* Source : [TPTP] *)
+(* Names : *)
+(* Status : Unsatisfiable *)
+(* Rating : 0.00 v2.7.0 *)
+(* Syntax : Number of clauses : 2 ( 0 non-Horn; 2 unit; 1 RR) *)
+(* Number of atoms : 2 ( 2 equality) *)
+(* Maximal clause size : 1 ( 1 average) *)
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+(* Number of functors : 4 ( 2 constant; 0-2 arity) *)
+(* Number of variables : 3 ( 0 singleton) *)
+(* Maximal term depth : 4 ( 2 average) *)
+(* Comments : A UEQ part of GRP085-1 *)
+(* Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply (multiply (multiply A B) C) (inverse (multiply A C))) B.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+autobatch paramodulation timeout=100;
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)